Question

Solve the equation by factoring: x^2 + 13x = -42
Show your work and check your answer.

Answer 1

x = - 7 or x = - 6

Explanation:

x^2 + 13x = -42

x² + 13x + 42 = 0

The key to factorization method is to break the second term into two; whose product gives the product of the first term and the third term.

That is,

13x = (7x + 6x)

(42×x²) = (7x)(6x)

x² + 13x + 42 = 0

x² + 7x + 6x + 42 = 0

x(x + 7) + 6(x + 7) = 0

(x + 6)(x + 7) = 0

Either (x+7) = 0 or (x+6) = 0

x = - 7 or x = - 6

Hope this Helps!!!

Answer 2

x=-6, -7

Explanation:

x^2+13x=-42

x^2+13x-(-42)=0

x^2+13x+42=0

factor out the trinomial,

find two numbers that when they multiply,

you get the third term, which is 42 in this case.

And when you add them, you get the second term, which is 13 in this case.

(x+6)(x+7)=0

zero property

x+6=0, x+7=0,

x=0-6=-6

x=0-7=-7